Mirrored mesh deforms unexpectedly and becomes uneven when rendered
I'm not sure about this answer, but to me it looks like a calculation approximation problem: if you add a subsurf modifier to the body mesh, even with only 1 step of subsurf, everithing goes allright (then you can apply it, to get a pure mesh). Blender is not intended as CAD and your mesh is very low poly, maybe also adding some loopcuts would resolve your odd behaviour. 

Consider that, generally, we use a circle of vertex for shaping the "hole" of eyes.

Hope it's useful.